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Sums of random multiplicative functions over function fields with few irreducible factors

Published online by Cambridge University Press:  28 February 2022

DAKSH AGGARWAL
Affiliation:
Department of Mathematics, Grinnell College, 1115 8th Ave # 3011, Grinnell, IA, USA, 50112 e-mail: aggarwal2@grinnell.edu
UNIQUE SUBEDI
Affiliation:
Department of Statistics, University of Michigan, 1085 University Ave, 323 West Hall, Ann Arbor, MI, USA, 48109 e-mail: subedi@umich.edu
WILLIAM VERREAULT
Affiliation:
Département de Mathématiques et de Statistique, Université Laval, Québec, QC, G1V 0A6, Canada e-mail: william.verreault.2@ulaval.ca
ASIF ZAMAN
Affiliation:
Department of Mathematics, University of Toronto, 40 St. George Street, Room 6290, Toronto, ON, Canada, M5S 2E4 e-mail: zaman@math.toronto.edu
CHENGHUI ZHENG
Affiliation:
Department of Statistics, University of Toronto, 100 St.George Street, Toronto, ON, Canada, M5S 3G3 e-mail: chenghui.zheng@mail.utoronto.ca

Abstract

We establish a normal approximation for the limiting distribution of partial sums of random Rademacher multiplicative functions over function fields, provided the number of irreducible factors of the polynomials is small enough. This parallels work of Harper for random Rademacher multiplicative functions over the integers.

Type
Research Article
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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